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3 years ago

Nathaniel pays $56 for 4 tickets to bucs games . What is the unit rate

Mathematics

1 answer:

marishachu [46]3 years ago

3 0

Answer: $14 per ticket

Step-by-step explanation:

56/4=14

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If w = 5 cos (xy) − sin (xz) and x = 1/t , y = t, z = t^3 ; then find dw/dt

Scrat [10]

In this question, we find the derivatives, using the chain's rule.

Doing this, the derivative is:

$\frac{dw}{dt} = \frac{5}{t}(\sin{1} - \cos{1}) - 2t\cos{t^2}$

Chain Rule:

Suppose we have a function $w(x,y,z), x = x(t), y = y(t), z = z(t)$ , and want to find it's derivative as function of t. It will be given by:

$\frac{dw}{dt} = \frac{dw}{dx}\frac{dx}{dt} + \frac{dw}{dy}\frac{dy}{dt} + \frac{dw}{dz}\frac{dz}{dt}$

Thus, we have to find the desired derivatives, which are:

w of x:

$\frac{dw}{dx} = -5y\sin{(xy)} - z\cos{(xz)}$

Considering $x = \frac{1}{t}, y = t, z = t^3$

$\frac{dw}{dx} = -5t\sin{(1)} - t^3\cos{(t^2)}$

w of y:

$\frac{dw}{dy} = -5x\cos{(xy)}$

Considering $x = \frac{1}{t}, y = t$

$\frac{dw}{dy} = -\frac{5}{t}\cos{1}$

w of z:

$\frac{dw}{dz} = -x\cos{(xz)}$

Considering $x = \frac{1}{t}, z = t^3$

$\frac{dw}{dz} = -\frac{1}{t}\cos{(t^2)}$

Derivatives of x, y and z as functions of t:

$\frac{dx}{dt} = -\frac{1}{t^2}$

$\frac{dy}{dt} = 1$

$\frac{dz}{dt} = 3t^2$

Derivative of w as function of t.

Now, we just replace what we found into the formula. So

$\frac{dw}{dt} = \frac{dw}{dx}\frac{dx}{dt} + \frac{dw}{dy}\frac{dy}{dt} + \frac{dw}{dz}\frac{dz}{dt}$

$\frac{dw}{dt} = (-5t\sin{(1)} - t^3\cos{(t^2)})(-\frac{1}{t^2}) - (\frac{5}{t}\cos{1}) - (\frac{1}{t}\cos{(t^2)})3t^2$

Applying the multiplications:

$\frac{dw}{dt} = \frac{5}{t}\sin{1} + t\cos{t^2} - \frac{5}{t}\cos{1} - 3t\cos{t^2}$

Applying the simplifications:

$\frac{dw}{dt} = \frac{5}{t}(\sin{1} - \cos{1}) - 2t\cos{t^2}$

Which is the derivative.

For more on the chain rule, you can check brainly.com/question/12795383

8 0

3 years ago

G(8.3,-1.4) is the midpoint between B(x,y) and L(-5.9,8). Find the coordinates of B

Dominik [7]

The coordinates of B is (22.5, -3.6)

<h3>How to find the coordinates of B?</h3>

The points are given as:

G = (8.3,-1.4)

B = (x,y)

L = (-5.9,8).

The midpoint is calculated as:

G = 0.5 * (x1 + x2, y1 + y2)

So, we have:

(8.3,-1.4) = 0.5 * (x - 5.9, y + 0.8)

This gives

(16.6,-2.8) = (x - 5.9, y + 0.8)

Solve for x and y

x - 5.9 = 16.6

y + 0.8 = -2.8

Evaluate

x = 22.5

y = -3.6

Hence, the coordinates of B is (22.5, -3.6)

Read more about midpoints at:

brainly.com/question/25886396

#SPJ1

4 0

2 years ago

Please help I’ll give more if it’s right plewseeee help me out

AleksAgata [21]

7 is the answer hopefully helps !!

4 0

3 years ago

Help pleasee asap! im super confused

dem82 [27]

Answer:

x = 4

Step-by-step explanation:

A midpoint divides the segment into two equal parts. Each is half the length of the whole.

XY = (1/2)XZ

5x+4 = (1/2)(8x +16)

5x +4 = 4x +8

x = 4 . . . . . . . . . subtract 4x+4 from both sides

_____

<em>Check</em>

5x+4 = 5(4)+4 = 24

8x+16 = 8(4) +16 = 48

So, XY is half of XZ.

7 0

3 years ago

Zach spent 2/3 hour reading on Friday and 1 1/3 hours reading on Saturday. How much more time did he read on Saturday than on Fr

hodyreva [135]

Subtract.

1 1/3 - 2/3

Convert 1 1/3 into an improper fraction:

4/3 - 2/3

Subtract the numerators together:

2/3

So he read 2/3 more time on Saturday than on Friday.

7 0

4 years ago

Read 2 more answers